Solve 2log_{a}y+2(log_{a}z-5log_{a}w)

$$2 \log _ { a } y + 2 ( \log _ { a } z - 5 \log _ { a } w )$$

Factor

$$\frac{2\left(\ln(y)+\ln(z)-5\ln(w)\right)}{\ln(a)}$$

Solution Steps

Factor out 2.

$$2\left(\log_{a}\left(y\right)+\log_{a}\left(z\right)-5\log_{a}\left(w\right)\right)$$

Consider \ln(y)\times \frac{1}{\ln(a)}+\ln(z)\times \frac{1}{\ln(a)}-5\ln(w)\times \frac{1}{\ln(a)}. Factor out \frac{1}{\ln(a)}.

$$\frac{\ln(y)+\ln(z)-5\ln(w)}{\ln(a)}$$

Rewrite the complete factored expression.

$$\frac{2\left(\ln(y)+\ln(z)-5\ln(w)\right)}{\ln(a)}$$

Evaluate

$$\frac{2\left(\ln(y)+\ln(z)-5\ln(w)\right)}{\ln(a)}$$